Rami Grossberg
Department of
Mathematical Sciences
Carnegie
Mellon University
Ph.D. Hebrew University of Jerusalem, 1986 (advisor: Saharon Shelah )
Research |
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Recent papers |
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Teaching |
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Model Theory Seminar |
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Some links |
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Personal Information |
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Research |
I'm interested in model theory (a branch of logic), especially in the classification theory of non elementary classes, infinitary logics, extensions of first-order logic, combinatorial set theory, and the applications of these areas to algebra.
What Shelah think of model theory? See Saharon Shelah's short article
John Baldwin wrote a
paper
containing survey of results and some problems that occupy me in
recent years.
My old and outdated
"official" page in our departmental catalog is here.
Former graduate students and
their postdoctoral positions (in chronological order):
1.
Olivier Lessmann.
Research Assistant Professor at University of Illinois at Chicago and EPSRC postdoc at Oxford University
PhD thesis: "Dependence relations in non elementary
classes" pdf 157 pages. Won the The Hugh D. Young
Graduate Student Teaching Award for 1996.
2.
Monica VanDieren. Szego Assistant Professor at Stanford and T.H.Hildebrandt Assistant
Professor at the University
of Michigan. PhD thesis: "Categoricity and Stability in
Abstract Elementary Classes" pdf
130 pages.
3.
Alexei Kolesnikov.
Assistant Professor at University
of Michigan. PhD thesis: "Generalized amalgamation in Simple
theories and characterization of dependence in non-elementary classes" pdf 107
pages. Won
the Eberly teaching prize for 2001, the top university prize for graduate
students.
4.
Will Boney.
Benjamin Peirce Fellow and NSF Postdoctoral Fellow at Harvard University.
PhD thesis: "Advances in Classification Theory for Abstract Elementary
Classes" pdf 162 pages.
5.
Sebastien Vasey.
Benjamin Peirce Fellow at Harvard University. PhD thesis: "Superstability and
Categoricity in Abstract Elementary Classes" pdf 572 pages. The Guy C. Berry Graduate Student Research Award and The Sacks Prize
for 2017, for more information
6.
Marcos Mazari-Armida. Burnett
Meyer Postoctoral Fellow, University of Colorado,
Boulder University of
Colorado. PhD thesis: "Remarks on classification theory for
abstract elementary classes with applications to abelian group theory and ring
theory" pdf 259 pages. A recording of the thesis defense is made
available on June 17, 2021. Passcode: 7+yA.HRR
Won the Sacks Prize for 2021.
The Sacks Prize is awarded for the best dissertation of the year in logic. For more information
A nice article about the research of Marcos Mazari-Armida
at the Colorado Arts and Sciences Magazine
7. Hanif J. Cheung.
PhD thesis: "Notions of amalgamation for abstract elementary classes"
pdf 82 pages. A recording of the thesis defense is made
available on June 24, 2022. Passcode: 6v#EVfz=
Further information will be
posted by September.
8.
Samson Leung ,
Defended thesis on November 17th, 2022. Recording of the defense: https://cmu.zoom.us/rec/share/OmI-mx9ipyYpIuZOZ2Jlk7qLxzv3Exlf8uEZBtc1B1fPNOvFiISuatVzeGBjOt7i.RCYEHuhR_e4eJC6A
Passcode: Y3LYP&z# Won the departmental prize
for excellence in research for 2022 and the The Hugh D. Young Graduate Student
Teaching Award for 2022. STABILITY,
CATEGORICITY AND AXIOMATIZATION OF ABSTRACT ELEMENTARY CLASSES pdf 194 pages.
9.
Wentao Yang https://wen-tao-y.github.io
Researcher at Inner Mongolia University, China.
Defended in
April 2024. Thesis title: “On successive
categoricity, stability and NIP in abstract elementary classes”. 75 pages. Copy available from http://www.math.cmu.edu/~rami/Wentao.final_thesis.pdf
Current PhD students:
· Jeremy
Beard
· Jin Xi Li
· Mick
Walker
Papers and theses written by PhD students while working under my guidance
Recent papers |
Downloading files
in the DVI or PDF formats is much faster since they are only 30-40% of the size
of PS files. The files are optimized for PDF.
(c) All material accessible
through this page is copyright by Rami Grossberg and his coauthors and by the
corresponding publishers. Permission is granted for fair use in personal,
noncommercial, and academic projects.
1.
Rami
Grossberg and Saharon Shelah. On universal
locally finite groups, Israel Journal of Mathematics, 41, (1983) 289--302.
2.
Rami
Grossberg. Models with second order properties in successors of singulars,
Journal of Symbolic Logic, 54, (1989) 122--137. pdf file from JSTOR
3.
Rami
Grossberg and Saharon Shelah. On the number
of non isomorphic models of an infinitary theory
which has the order property Part A, Journal of Symbolic Logic, 51, (1986)
302--322. pdf file from JSTOR
4.
Rami
Grossberg and Saharon Shelah. A
non-structure theorem for a theory which has the unsuperstability
property, Illinois J. of Mathematics, 30, (1986) 364--390.
5.
Rami
Grossberg. A downward L\"{o}wenheim Skolem theorem for theories which have the unsuperstability property, Journal of Symbolic Logic, 53,
(1988) 231--242. pdf file from JSTOR
6.
Rami
Grossberg and Saharon Shelah. On the
structure of $Ext_p(G,{\bf Z})$, Journal of Algebra, 121, (1989) 117--128.
7.
Rami
Grossberg and Bradd Hart.
The classification theory of excellent classes, Journal of Symbolic Logic, 54,
(1989) 1359--1381. pdf file from JSTOR
8.
Michael
Albert and Rami Grossberg. Rich models,
Journal of Symbolic Logic, 55, (1990) 1292--1298. pdf file from JSTOR
9.
Michael
Albert and Rami Grossberg. Characterizing
stability and superstability by unions of chains and saturated models, Research
Report No. 89-47, May 1989. pdf file
10.
Rami
Grossberg. Indiscernible sequences in a model which fails to have the order
property, Journal of Symbolic Logic, 56 (1991) 115--123. pdf file from JSTOR
11.
Rami Grossberg.
On chains of relatively saturated submodels of a
model without the order property, Journal of Symbolic Logic, 56, (1991)
123--128. pdf file from JSTOR
12.
Rami
Grossberg. Review of Wilfried Hodges's book -- "Building models by
games", Journal of Symbolic Logic, 56 (1991) 752--753. pdf file from JSTOR
13.
Martin Goldstern, Rami
Grossberg and Menachem
Kojman. Infinite homogeneous bipartite
graphs with unequal sides, Discrete Mathematics 149 (1996) 69-82. ps , dvi ,
pdf .
14.
Saharon Shelah and Rami Grossberg. On
cardinalities in quotients of inverse limits of groups, Mathematica
Japonica. 47 (1998), no. 2, 189-197. ps , dvi ,
pdf .
15.
John T. Baldwin,
Rami Grossberg and Saharon Shelah. A
characterization of the finite cover property and stability, Journal of
Symbolic Logic 64 (1999) 678-684. ps , dvi ,
pdf .
16.
Rami
Grossberg and Saharon Shelah. On Hanf numbers of the infinitary order property. 19
pages, DRAFT revised on 6/9/98. ps , dvi ,
pdf .
17.
Doug Ensley
and Rami Grossberg. Ramsey's theorem in stable structures, 37 pages,
last revision 8/4/1995. [Containing a start of forking via averages of
sequences in finite relational structures] pdf .
18.
Doug Ensley
and Rami Grossberg. Ramsey's theorem in stable structures, 21 pages, last
revision 5/15/97. [This is a truncated w/o model theory version of the above] ps , dvi ,
pdf .
19.
Rami
Grossberg and Olivier
Lessmann. Dependence Relation in Pregeometries, Algebra Univesalis 44 (2000) pp 199-216. The published paper from Birkhauser's site. ps ,
dvi
, https://www.math.cmu.edu/~rami/pregeo.pdf
20.
Rami
Grossberg and Olivier
Lessmann. The local order property in non elementary classes, Arch Math Logic 39 (2000) 6,
439-457. The published paper from Springer's site. ps , dvi
, pdf .
21.
Rami
Grossberg, José
Iovino and Olivier Lessmann. A primer of
simple theories, Archive of Math Logic, 41, (2002), 541-580. The published paper from Springer's site. ps , dvi ,
pdf
.
22.
Rami
Grossberg and Olivier
Lessmann. Shelah's stability spectrum
and homogeneity spectrum in finite diagrams, Arch. Math. Logic 41 (2002) 1,
1-31. The published paper from Springer's site. ps , dvi
, pdf .
23.
Rami
Grossberg. Classification theory for abstract elementary classes, Logic
and Algebra, ed. Yi Zhang, Contemporary Mathematics, Vol 302, AMS, (2002),
pp. 165--204. ps , https://www.math.cmu.edu/~rami/Rami-NBilgi.pdf
24.
Rami
Grossberg, Alexei
Kolesnikov, Ivan
Tomasic and Monica VanDieren. The equality S1=D=R, Mathematical
Logic Quaterly, 49, (2003), 115-128. pdf file from the publisher Wiley InterScience
.
25.
Rami
Grossberg and Olivier
Lessmann. Abstract decomposition
theorem and applications, Contemporary Mathematics, Vol 380, (2005), AMS,
pp. 73--108. ps , pdf .
26.
Rami
Grossberg and Monica VanDieren. Shelah's
Categoricity Conjecture from a successor for Tame Abstract Elementary Classes. Journal
of Symbolic Logic, Vol 71 (2006) 2, 553--568. ps , pdf .
27.
Rami
Grossberg and Monica VanDieren. Galois-stability
for Tame Abstract Elementary Classes. Journal of Mathematical Logic, Vol.
6, No. 1 (2006) 25--49. ps , pdf .
28.
Rami
Grossberg and Monica VanDieren. Categoricity
from one successor cardinal in Tame Abstract Elementary Classes. Journal of
Mathematical Logic, Vol. 6, No. 2 (2006) 181--201. ps , pdf .
29.
Rami
Grossberg and Alexei
Kolesnikov. Superior Abstract Elementary Classes are Tame. 26 pages, last updated 9/9/05. ps , pdf .
submitted.
30.
Rami
Grossberg, Monica VanDieren and Andrés Villaveces. Uniqueness of Limit Models in
Classes with Amalgamation. pdf . Mathematical Logic Quarterly - Vol.62, Issue
4-5/2016, page 367-382.
31.
Will Boney
and Rami Grossberg. Forking in Short and Tame AECs. pdf . Ann. Pure Appl. Logic 168 (2017), no.
8, 1517--1551.
32.
Will Boney,
Rami Grossberg, Alexei
Kolesnikov and Sebastien Vasey. Canonical forking in AECs. pdf . Annals of Pure and Applied Logic 167 (2016), no. 7,
590--613.
33.
Rami
Grossberg, and Sebastien
Vasey. Equivalent definitions of superstability in tame abstract
elementary classes pdf . The Journal of Symbolic Logic 82 (2017), no. 4, 1387–1408. published version
34.
Will Boney,
Rami Grossberg, Michael
Lieberman , Jiri Rosicky and Sebastien Vasey. $\mu$-Abstract elementary classes and
other generalizations. Journal of Pure and Applied Algebra 220 (2016), no.
9, 3048--3066. published version, pdf .
35.
Will Boney,
Rami Grossberg, Monica VanDieren and Sebastien Vasey. Superstability
from categoricity in AECs. pdf . Annals of Pure and Applied Logic 168 no. 7
(2017)1383--1395. published version
36.
Rami
Grossberg and Marcos Mazari-Armida . Simple-like
independence relations in abstract elementary classes, Annals of Pure and
Applied Logic, Volume 172, Issue 7, (2021), 28 pages pdf published
version
I am working on three volume model theory book series:
· A course in Model Theory I: Introduction, 815 pages.
· A course in Model Theory II: Classification Theory, 233
pages.
· A course in Model Theory III: Classification Theory for
Abstract Elementary Classes, 205 pages.
For more information click here .
Note on PDF: Some ligatures may not display correctly on your screen, depending on your operating system. However, the output on a PostScript printer should be of excellent quality.
Teaching |
Spring, 2020 |
Fall, 2020 |
Spring, 2021 |
Fall, 2021 |
Spring, 2022 |
Fall, 2022 |
Model Theory Seminar |
Little before fall
1992 I started a Mathematical Logic Seminar and managed it until fall 2002. I
am not responsible for that seminar anymore, it is run
now in a different format than in the past by Ernest Schimmerling.
At present I am organizing a Model
Theory Seminar. Since the pandemic started in Spring 2020 we meet via zoom on Thursdays 11-12:30 PM. Before Covid
we used to meet on Mondays 5-6:30PM in WeH 7201. We
may return to this schedule in January 2023. Information about current and past
talks can be found here.
Some links |
· This
semester Will
Boney is teaching in Harvard a course titeled
Classification Theory for Tame Abstract Elementary Classes .
· Ariella: Most people think that girls can
not excel at engineering and math, but I dont
care what they say, I am going to be an engineer someday, From the Pittsburgh Post Gazette,
· A non-Erdos like interview with my boss,
· A workshop dedicated to Classification Theory for Abstract
Elementary Classes was held at the American Institute of Mathematics July 17 to
July 21 2006. More
information,
· A Condensed biography of Julia Robinson,
· The
CMU pure and applied logic home page,
· American
Mathematical Society,
· Association
for Symbolic Logic,
· Mathematics web sites around the world,
· Mathematical Logic around the world,
· National Research Council's ranking of PhD programs, last time updated
1994,
· Pictures I have taken in Bogota during BMMT
2003 , can be found here.
Personal |
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Rami@cmu.edu
Last modified: August 12, 2024. |